Stats_example_1.cpp

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//==============================================================================
//
//  This file is part of GNSSTk, the ARL:UT GNSS Toolkit.
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//==============================================================================
//
//  This software was developed by Applied Research Laboratories at the
//  University of Texas at Austin, under contract to an agency or agencies
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//==============================================================================
 
// An example of robust statistics found in lib/geomatics
// compute Robust statistics. Also demonstrate the use
// of random number generators.
 
#include <iostream>
#include <cstdlib>
#include <ctime>
 
#include "RobustStats.hpp"
#include "random.hpp"
#include "Stats.hpp"
 
using namespace std;
using namespace gnsstk;
using namespace Robust;
 
 
int main(int argc, char* argv[])
{
   double *s = nullptr;
   double mean = 10.0;
   double stdDev = 2.0;
   double badMeasurement = 10000;
 
   try
   {
 
         // Generate a set of random numbers that are normally distributed
      size_t N = 1000;
      s= new double[N];
 
      Stats<double> simpleStats;
 
      for (size_t i = 0; i<N; i++)
      {
         s[i] = RandNorm(stdDev)+mean;
            // Note the 1.0 keeps the math floating point,
            // otherwise the division is integer division.
 
         simpleStats.Add(s[i]);
      }
 
         // Show the sample mean and std deviation before adding
         // perturbed samples.
      cout  << endl << "Before perturbation: sample mean is               "
            << simpleStats.Average() << ", " << endl;
      cout  << "                     sample standard deviation is "
            << simpleStats.StdDev() << endl << endl;
 
         // Now perturb the sample data set with a "bad" measurement.
      srand(time(0));
      size_t i = (rand()%N);
      s[i] = badMeasurement;
      cout << "Altering measurement " << i << " to take the value of "
           << badMeasurement << endl;
 
         // Show how the sample mean and std deviation are altered.
      Stats<double> secondStats;
      for (size_t i = 0; i<N; i++)
      {
         secondStats.Add(s[i]);
      }
 
         // Show the sample mean and std deviation before adding
         // perturbed samples.
      cout  << endl << "After perturbation:  sample mean is                "
            << secondStats.Average() << ", " << endl;
      cout  << "                     sample standard deviation is "
            << secondStats.StdDev() << endl << endl;
 
      double median,mad,Q1,Q3;
 
      QSort(s,N);
      Robust::Quartiles(s,N,Q1,Q3);
      mad = Robust::MedianAbsoluteDeviation(s,N,median);
 
      cout << "Robust statistics:\n";
      cout << "                     number    = " << N << endl;
      cout << "                     quartiles = " << setw(11)
           << setprecision(8) << Q1
           << " " << setw(11) << setprecision(8) << Q3 << endl;
      cout << "                     median    = " << setw(11)
           << setprecision(8) << median << endl;
      cout << "                     MAD       = " << setw(11)
           << setprecision(8) << mad << endl;
 
 
         // Show how the sample mean and std deviation are altered.
      Stats<double> thirdStats;
      for (size_t i = 0; i<N; i++)
      {
         if ((fabs(s[i] - median)/mad)<8)
            thirdStats.Add(s[i]);
      }
 
 
         // Compute the mean and std deviation now given robust statistics.
      cout  << endl << "Using robust stats:  sample mean is                "
            << thirdStats.Average() << ", " << endl;
      cout  << "                     sample standard deviation is "
            << thirdStats.StdDev() << endl << endl;
 
   }
   catch (bad_alloc& b)
   {
      cerr << "Allocation error. Out of memory?" << endl;
      exit(1);
   }
 
      // Delete the dynamic array allocation.
      // (don't just rely on the operating system to do this).
   delete[] s;
   s = 0;
 
   return 0;
}